Categorical Evaluation Report
CDC FluSight Team
March 13, 2024
For the 2023-2024 influenza season, CDC called for national and jurisdiction categorical probability predictions for the direction and magnitude of changes in hospitalization rates per 100k population. The collection period began October 11, 2023 and will run through May 1, 2024.
This report is supported by work from colleagues in the Reich Lab at UMass-Amherst, Jessica Davis at Northeastern University, and Gursharn Kaur and Srini Venkatramanan at University of Virginia.
Categorical forecasts are evaluated using the Brier Score, Brier Skill Score, and Ranked Probability Score. All scores are defined below. Models presented include the FluSight-ensemble - an ensemble of submitted categorical forecasts and FluSight-equal_cat which is used as a baseline comparison and is comprised of equal probabilities (0.2) for each category in each jurisdiction each week.
Higher skill scores are better
Forecasts after 11/03/2023 are included.
Observed trends as of March 09, 2024
Trend from week T
T-1
For one-week ahead rate trends or the change from week T-1 to week T (horizon = 0):
Stable: forecasted changes in
hospitalizations qualify as stable if either the magnitude of the rate
change is less than 1/100k OR the corresponding magnitude of the count
change is less than 10.
Increase: positive forecasted changes
that do not qualify as stable and for which the forecasted rate change
is less than 2/100k.
Large increase: positive forecasted rate
changes that do not qualify as stable and for which the forecasted rate
change is larger than or equal to 2/100k.
Decrease: negative
forecasted rate changes that do not qualify as stable and for which the
magnitude of the forecasted rate change is less than 2/100k.
Large decrease: negative forecasted rate changes that do not
qualify as stable and for which the magnitude of the forecasted rate
change is larger than or equal to 2/100k.
T-2
For two-week ahead rate trends or the change from week T-2 to week T (horizon = 1):
Stable: forecasted changes in
hospitalizations qualify as stable if either the magnitude of the rate
change is less than 1/100k OR the corresponding magnitude of the count
change is less than 10.
Increase: positive forecasted changes
that do not qualify as stable and for which the forecasted rate change
is less than 3/100k.
Large increase: positive forecasted rate
changes that do not qualify as stable and for which the forecasted rate
change is larger than or equal to 3/100k.
Decrease: negative
forecasted rate changes that do not qualify as stable and for which the
magnitude of the forecasted rate change is less than 3/100k.
Large decrease: negative forecasted rate changes that do not
qualify as stable and for which the magnitude of the forecasted rate
change is larger than or equal to 3/100k.
T-3
For three-week ahead rate trends or the change from week T-3 to week T (horizon = 2):
Stable: forecasted changes in
hospitalizations qualify as stable if either the magnitude of the rate
change is less than 2/100k OR the corresponding magnitude of the count
change is less than 10.
Increase: positive forecasted changes
that do not qualify as stable and for which the forecasted rate change
is less than 4/100k.
Large increase: positive forecasted rate
changes that do not qualify as stable and for which the forecasted rate
change is larger than or equal to 4/100k.
Decrease: negative
forecasted rate changes that do not qualify as stable and for which the
magnitude of the forecasted rate change is less than 4/100k.
Large decrease: negative forecasted rate changes that do not
qualify as stable and for which the magnitude of the forecasted rate
change is larger than or equal to 4/100k.
T-4
For four-week ahead rate trends or the change from week T-4 to week T (horizon = 3):
Stable: forecasted changes in
hospitalizations qualify as stable if either the magnitude of the rate
change is less than 2.5/100k OR the corresponding magnitude of the count
change is less than 10.
Increase: positive forecasted changes
that do not qualify as stable and for which the forecasted rate change
is less than 5/100k.
Large increase: positive forecasted rate
changes that do not qualify as stable and for which the forecasted rate
change is larger than or equal to 5/100k.
Decrease: negative
forecasted rate changes that do not qualify as stable and for which the
magnitude of the forecasted rate change is less than 5/100k.
Large decrease: negative forecasted rate changes that do not
qualify as stable and for which the magnitude of the forecasted rate
change is larger than or equal to 5/100k.
Brier Score and Ranked Probablity Score
Definitions
Let \(\{-2,-1,0,1,2\}\) be the numeric representation of the categories {“large_decrease”, “decrease”, “stable”, “increase”, “large_increase”}. Then for a model \(m\), location \(loc\), and horizon \(h\)
Brier score is given by: \[ BS(m, loc, h) = \sum_{i=-2}^2 \left(p(i)- p(i)\right)^2\] where \(p(i)\) and \(o(i)\) denotes the forecast probability and observed probability for category \(i\).
Ranked Probability Scores is given by: \[ RPS(m, loc, h) = \frac{1}{4}\sum_{i=-2}^2 \left( \hat{F}(i)- F(i)\right)^2\] where \(\hat{F}\) and \(F\) denotes the forecast CDF and observed CDF on the discrete state space \(\{-2,-1,0,1,2\}\).
Average Brier score (for a model \(m\) and location \(loc\)) is given by: \[ BS(m, loc) = \frac{1}{4} \sum_{h=0}^3 BS(m, loc, h)\]
Similarly, average RPS (for a model \(m\) and location \(loc\)) is given by: \[ RPS(m, loc) = \frac{1}{4} \sum_{h=0}^3 RPS(m, loc, h)\]
Skill scores are taken as 1 minus the pairwise geometric mean of a particular model (compared to all other submitted models) over the pairwise geometric mean of the equal probability model.
Example: BS vs RPS
Evaluation Metrics
Brier Skill Comparison
RPSS Comparison
Metrics by model
Brier
Horizon 0
Horizon 1
Horizon 2
Horizon 3
RPS
Horizon 0
Horizon 1
Horizon 2
Horizon 3
Evaluation by location
Brier Skill Score
Ranked Probability Skill Score
Forecast trend for reference date March 09, 2024
Probability of any increase
Probability of any decrease
Evaluation Periods
